1. Odwalla's OJ is packaged in 250 ml bottles and has a process standard deviation of
10 ml. In monitoring the fill process, 6 samples (of 25 bottles each) were collected and averaged.
|
Sample
|
Sample mean
|
|
sl
|
249
|
|
s2
|
252
|
|
s3
|
253
|
|
s4
|
248
|
|
s5
|
245
|
|
s6
|
253
|
a) What is the total number of bottles sampled?
b) What is the standard deviation of the distribution of sample means?
c) Compute the 3-sigma control limits. Is the process in control, given these control limits? Why/Why not?
d) Compute the 2-sigma control limits. Is the process in control, given these control limits? Why/Why not?
2. A state department of tourism and recreation collects data on the number of cars with out-of-state license plates in a state park. (The group's position is that more out-of-state plates means the state's advertising programs are working.) The sample size is fixed at n=100 each day. Data from the previous 20 days indicate the following number of out-of-state license plates:
|
Day
|
Plates
|
Day
|
Plates
|
Day
|
Plates
|
Day
|
Plates
|
|
1
|
24
|
6
|
31
|
11
|
22
|
16
|
22
|
|
2
|
33
|
7
|
15
|
12
|
15
|
17
|
34
|
|
3
|
18
|
8
|
18
|
13
|
25
|
18
|
10
|
|
4
|
21
|
9
|
23
|
14
|
33
|
19
|
23
|
|
5
|
26
|
10
|
13
|
15
|
16
|
20
|
13
|
a) Calculate the overall proportion of "tourists" (cars with out-of-state plates).
b) Calculate the LCL and UCL for these data.
c) Plot the control chart. Are all points within the control limits?
3. Ten samples of size four were taken from a process, and their weights measured. The sample avenges and sample ranges are in the following table. Construct and plot an X-bar and R-chart using these data. Is the process in control?
|
Sample
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
Mean
|
20.01
|
19.98
|
20.25
|
19.9
|
20.35
|
19.23
|
20.01
|
19.98
|
20.56
|
19.97
|
|
Range
|
0.45
|
0.67
|
0.3
|
0.3
|
0.36
|
0.49
|
0.53
|
0.4
|
0.95
|
0.79
|
4. Western Airlines merged with a smaller airline recently. Every day since the merger, a random sample of 30 Western flights has been analyzed. A flight that takes off more than 10 minutes after its scheduled departure time is considered to be late; otherwise, it is not late. Western's performance over the past 10 days is shown in the table below.
|
Day
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
# Late Flights
|
4
|
2
|
5
|
9
|
2
|
3
|
3
|
1
|
2
|
8
|
What are the 95.5% control limits for p, the true percentage of late flights? No chart is required. Has Western Airlines' on-time performance been in-control over the last 2 weeks? Explain briefly. (0.7%, 25.3%; no, it's been out-of-control as 2 of the 10 samples are above the UCL.)
5. A carpet manufacturer wishes to set up a c-chart for its manufacturing process. It inspects 10 carpets at random, and notes the number of defects in each carpet, as follows.
|
Carpet #
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
# of defects
|
2
|
3
|
0
|
2
|
1
|
2
|
1
|
3
|
4
|
2
|
a) Determine two-sigma control limits for the mean number of defects per carpet.
b) Three carpets are subsequently inspected, and the # of defects are 1, 6, 2. Is the process in control? Explain why.
6. A gourmet coffee shop in downtown SF is open 200 days a year and sells an average of 75 pounds of Kona Coffee beans a day. (Demand can be assumed to be distributed normally with a standard deviation of 15 pounds/day.) After ordering (fixed cost = S16 per order), beans are always shipped from Hawaii within exactly 4 days. Per-pound annual holding costs for the beans are 53.
a) What is the economic order quantity (EOQ) for Kona coffee beans?
b) What are the total annual holding costs of cycle stock for Kona coffee beans?
c) What are the total annual fixed ordering costs for Kona coffee beans?
d) Assume that management has specified that no more than a 1% risk during stock out is acceptable. What should our reorder point RCM be?
e) What is the safety stock need to attain a 1% risk of stock-out during lead time?
f) What is the annual holding cost of maintaining the level of safety stock needed to support a 1% risk?
g) If management specified that a 2% risk of stock-out during lead time would be acceptable, would our safety stock holding costs decrease or increase?